Alternating group:A5

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This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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This particular group is the smallest (in terms of order): simple non-Abelian group

Definition

The alternating group A_5 is defined in the following ways:

Group properties

Subgroups

Endomorphisms

Bigger groups

Groups having it as a subgroup

The alternating group is a subgroup of index two inside the symmetric group on five elements. It is also of index two in the full icosahedral symmetry group, which turns out not to be S_5, but instead the direct product of A_5 and the cyclic group of order two.

Groups having it as a quotient

The alternating group is a quotient of SL(2,5) by its center. Hence, it is the inner automorphism group of SL(2,5). SL(2,5) is also the universal central extension of the alternating group.


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